Acoustic logs are routinely used in the oil and gas industry to characterize the formation around a borehole, e.g., by identifying various types of lithology (such as shale or sandstone), detecting the presence of hydrocarbons, or measuring certain geophysical properties such as stress or permeability. To acquire an acoustic log, a sonic logging tool with one or more acoustic sources and multiple receivers may be run through the borehole (e.g., on a wireline or as part of a bottom hole assembly of a drill string) to excite acoustic waves in the formation and measure the formation response with the receivers at various depths along the borehole. For each depth, the acoustic waveforms acquired by the various receivers may be processed with a semblance (or, as it is also often referred to, beamforming) method to compute a two-dimensional (e.g., time-slowness or frequency-slowness) semblance map that generally exhibits peaks corresponding to the arrivals of various types of acoustic waves (such as compressional, refracted-shear, and Stoneley waves) travelling at different apparent velocities. The identified peaks may be aggregated across depths to obtain, for each type of wave, a log of the wave velocity or slowness (which is the inverse of the velocity) as a function of depth within the borehole.
While a sole signal peak in a semblance map can usually be easily detected based on an associated maximum value of the semblance function, the simultaneous detection and identification of multiple signal peaks can be more challenging. Coherence-based semblance methods can be very sensitive, but accidentally “detect” signals that are not real. In such cases, the fake alarm of detecting these “signals” is due simply to a random occurrence of energy crossing the receiver array that happens to be “coherent enough” to be detected. Consequently, coherence-based methods often need additional constraints, based on physics, to separate out real detections from false alarms. Conversely, amplitude-based semblance methods are more robust, but are prone to false negatives, i.e., the failure to detect a real signal. Missed detections are often due to signal-amplitude levels too small compared with some reference amplitude level, such as, e.g., the highest signal amplitude within the semblance map, upon which the threshold amplitude for signal detection may be based. The problem often arises when trying to simultaneously detect multiple signals with widely varying amplitudes. In acoustic borehole data, for example, the signal peak associated with the arrival of the compressional wave is sometimes orders of magnitudes lower than that of the Stoneley wave, rendering the selection of a suitable detection threshold difficult, especially when the noise levels change from one borehole depth to the next. Accordingly, improved methods for the simultaneous detection of multiple signals in semblance maps, with low rates of both false positives and false negatives, are desirable.